<title>Deriving the inverse square law from radiative transfer equations</title>

Abstract

The radiative transfer equation (RTE) is the fundamental equation of the radiative transfer theory and one of more important theoretical tools in biomedical optics for describing light propagation in biological tissues. The RTE assumes that the refractive index of the medium is constant and the ray divergence is zero. These assumptions limit its range of applicability. To eliminate this drawback three new RTE have been proposed recently. Obviously, those equations must be carefully studied and compared. With that aim we solve the standard RTE and the new radiative transfer equations for the specific case of a time-independent isotropic point source in an infinite non-absorbing non-amplifying non-scattering linear medium with constant refractive index. The solution to this problem is the well-known inverse square law of geometrical optics. We show that only one of those equations gives solutions consistent with the inverse square law for the irradiance, due to its ability to model non-negligible ray divergence near a point source.